Cloud Energetic Classification and Edge Dynamics within the Thermodynamic Manifold Framework — Supplementary Note S1 with Software (v3.0)

This deposit contains the Supplementary Note S1 and accompanying open-source software (cloud_manifold_v3_0.py) for the cloud energetic classification module of the Thermodynamic Manifold Framework (TMF). The note introduces a dimensionless cloud energy ratio R = F_dyn / F_rad, shows that ERA5 atmospheric observations are constrained to a curved surface R_max(T,C) in (T, C, R) state space, and characterises the edge dynamics at the physical boundary ρ = R / R_max = 1. Key empirical results from ERA5 (1980–2025, n = 16.3M): - Parametric envelope fit R² = 0.937 - Asymmetry index AI = +0.111 (slow build-up, fast collapse), n = 700,269 events - Spontaneous organisation threshold at ρ ≈ 0.75 - Probabilistic state estimator P(regime | ρ, T, C, k) Related TMF paper: https://doi.org/10.5281/zenodo.19430594